Internal problem ID [14683]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y=108 t} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(diff(y(t),t$4)-6*diff(y(t),t$3)+13*diff(y(t),t$2)-24*diff(y(t),t)+36*y(t)=108*t,y(t), singsol=all)
\[ y \left (t \right ) = \left (t c_{4} +c_{2} \right ) {\mathrm e}^{3 t}+\cos \left (2 t \right ) c_{1} +c_{3} \sin \left (2 t \right )+3 t +2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 41
DSolve[y''''[t]-6*y'''[t]+13*y''[t]-24*y'[t]+36*y[t]==108*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 t+c_4 e^{3 t} t+c_3 e^{3 t}+c_1 \cos (2 t)+c_2 \sin (2 t)+2 \]